Question

How do you solve $\left|x-6\right|=10$?

Answer 1

Step-1: Define modulus function:

The modulus of function is defined as $\left|x\right|=\left\{\begin{array}{ll}x& x\ge 0\\ -x& x<0\end{array}\right.$.

Apply the definition of modulus in the equation $\left|x-6\right|=10$.

There are two cases, first $\left(x-6\right)=10$ and second $-\left(x-6\right)=10$.

Step-2: Solving $\left(x-6\right)=10$:

$$\begin{gathered} x-6=10 \\ \Rightarrow x-6=10 \\ \Rightarrow x=10+6\left(\mathrm{Adding}6\mathrm{to}\mathrm{both}\mathrm{sides}\right) \\ \therefore x=16 \end{gathered}$$

Step-3: Solving $-\left(x-6\right)=10$:

$\begin{array}{rcl}-\left(x-6\right)& =& 10\\ & \Rightarrow & -x+6=10\\ & \Rightarrow & -x=10-6\left(\mathrm{Subtracting}6\mathrm{from}\mathrm{both}\mathrm{sides}\right)\\ & \Rightarrow & -x=4\\ \therefore x& =& -4\end{array}$

Therefore, the value of $x$ is $-4$ and $16$.